Question

∠1 and ∠2 are vertical angles. if m∠1=(17x + 1)° and m∠2=(20x - 14)°, find m∠2

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, $m\angle1 = m\angle2$.
$17x + 1=20x-14$

Step2: Solve for $x$

Subtract $17x$ from both sides:
$17x + 1-17x=20x-14 - 17x$
$1 = 3x-14$
Add 14 to both sides:
$1+14=3x-14 + 14$
$15 = 3x$
Divide both sides by 3:
$\frac{15}{3}=\frac{3x}{3}$
$x = 5$

Step3: Find $m\angle2$

Substitute $x = 5$ into the expression for $m\angle2$:
$m\angle2=(20x - 14)^{\circ}=(20\times5-14)^{\circ}$
$=(100 - 14)^{\circ}=86^{\circ}$

Answer:

$86^{\circ}$